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Elements of the group are displayed as permutations of degree 36.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $C_3^7.S_3^2\wr C_2$ | 1A | $1$ | $1$ | $C_3^7.S_3^2\wr C_2$ | 1A | 1A | $()$ |
| $C_3^7.S_3^2\wr C_2$ | 2A | $2$ | $54$ | not computed | 1A | 2A | $(4,10)(5,11)(6,12)(16,22)(17,24)(18,23)(28,34)(29,35)(30,36)$ |
| $C_3^7.S_3^2\wr C_2$ | 2B | $2$ | $54$ | not computed | 1A | 2B | $(4,10)(5,12)(6,11)(16,34)(17,35)(18,36)(22,28)(23,30)(24,29)$ |
| $C_3^7.S_3^2\wr C_2$ | 2C | $2$ | $162$ | not computed | 1A | 2C | $(5,6)(11,12)(16,28)(17,29)(18,30)(22,34)(23,36)(24,35)$ |
| $C_3^7.S_3^2\wr C_2$ | 2D | $2$ | $729$ | not computed | 1A | 2D | $(1,8)(2,9)(3,7)(4,11)(5,10)(6,12)(13,32)(14,31)(15,33)(16,36)(17,34)(18,35)(19,26)(20,27)(21,25)(22,30)(23,29)(24,28)$ |
| $C_3^7.S_3^2\wr C_2$ | 2E | $2$ | $729$ | not computed | 1A | 2E | $(1,20)(2,21)(3,19)(4,24)(5,23)(6,22)(7,25)(8,26)(9,27)(10,28)(11,30)(12,29)(13,33)(14,31)(15,32)(16,36)(17,35)(18,34)$ |
| $C_3^7.S_3^2\wr C_2$ | 2F | $2$ | $1458$ | not computed | 1A | 2F | $(1,9)(2,7)(3,8)(4,24)(5,23)(6,22)(10,30)(11,29)(12,28)(13,31)(14,33)(15,32)(16,35)(17,34)(18,36)(19,26)(20,27)(21,25)$ |
| $C_3^7.S_3^2\wr C_2$ | 2G | $2$ | $2916$ | not computed | 1A | 2G | $(1,34)(2,35)(3,36)(4,9)(5,7)(6,8)(10,14)(11,15)(12,13)(16,20)(17,19)(18,21)(22,26)(23,25)(24,27)(28,32)(29,31)(30,33)$ |
| $C_3^7.S_3^2\wr C_2$ | 2H | $2$ | $4374$ | not computed | 1A | 2H | $(1,21)(2,20)(3,19)(5,6)(7,13)(8,15)(9,14)(10,35)(11,36)(12,34)(16,30)(17,28)(18,29)(22,23)(25,31)(26,33)(27,32)$ |
| $C_3^7.S_3^2\wr C_2$ | 2I | $2$ | $4374$ | not computed | 1A | 2I | $(1,25)(2,26)(3,27)(4,10)(5,11)(6,12)(7,8)(13,14)(16,22)(17,24)(18,23)(19,31)(20,32)(21,33)(28,34)(29,35)(30,36)$ |
| $C_3^7.S_3^2\wr C_2$ | 2J | $2$ | $6561$ | not computed | 1A | 2J | $(1,13)(2,14)(3,15)(5,6)(7,31)(8,33)(9,32)(10,35)(11,36)(12,34)(16,30)(17,28)(18,29)(20,21)(22,23)(26,27)$ |
| $C_3^7.S_3^2\wr C_2$ | 3A | $3$ | $4$ | $C_3^5.C_3^4.C_6^2.C_2$ | 3A | 1A | $(4,5,6)(10,11,12)(16,17,18)(22,24,23)(28,30,29)(34,36,35)$ |
| $C_3^7.S_3^2\wr C_2$ | 3B | $3$ | $4$ | $C_3^5.C_3^4.C_6^2.C_2$ | 3B | 1A | $(4,6,5)(10,11,12)(16,18,17)(22,24,23)(28,29,30)(34,36,35)$ |
| $C_3^7.S_3^2\wr C_2$ | 3C | $3$ | $4$ | $C_3^7.C_3\wr D_4$ | 3C | 1A | $(1,3,2)(4,5,6)(7,9,8)(10,12,11)(13,14,15)(16,17,18)(19,20,21)(22,23,24)(25,26,27)(28,30,29)(31,33,32)(34,35,36)$ |
| $C_3^7.S_3^2\wr C_2$ | 3D | $3$ | $4$ | $C_3^7.C_3\wr D_4$ | 3D | 1A | $(1,3,2)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,17,18)(19,21,20)(22,24,23)(25,26,27)(28,30,29)(31,32,33)(34,36,35)$ |
| $C_3^7.S_3^2\wr C_2$ | 3E | $3$ | $8$ | $C_3^5.C_3^4.C_6^2$ | 3E | 1A | $(7,9,8)(19,20,21)(31,33,32)$ |
| $C_3^7.S_3^2\wr C_2$ | 3F | $3$ | $8$ | $C_3^5.C_3^4.C_6^2$ | 3F | 1A | $(1,2,3)(4,6,5)(7,8,9)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,23,24)(25,27,26)(28,29,30)(31,32,33)(34,35,36)$ |
| $C_3^7.S_3^2\wr C_2$ | 3G | $3$ | $16$ | $C_3^4.C_3^5.C_3.C_6$ | 3G | 1A | $(4,5,6)(7,9,8)(10,11,12)(16,17,18)(19,20,21)(22,24,23)(28,30,29)(31,33,32)(34,36,35)$ |
| $C_3^7.S_3^2\wr C_2$ | 3H | $3$ | $16$ | $C_3^4.C_3^5.C_3.C_6$ | 3H | 1A | $(4,5,6)(7,9,8)(10,12,11)(16,17,18)(19,20,21)(22,23,24)(28,30,29)(31,33,32)(34,35,36)$ |
| $C_3^7.S_3^2\wr C_2$ | 3I | $3$ | $16$ | $C_3^7.C_3^4.C_2$ | 3I | 1A | $(1,3,2)(10,11,12)(13,14,15)(22,24,23)(25,26,27)(34,36,35)$ |
| $C_3^7.S_3^2\wr C_2$ | 3J | $3$ | $36$ | not computed | 3J | 1A | $(16,18,17)(22,24,23)(28,30,29)(34,35,36)$ |
| $C_3^7.S_3^2\wr C_2$ | 3K | $3$ | $72$ | not computed | 3K | 1A | $(4,6,5)(10,12,11)(13,14,15)(16,18,17)(19,20,21)(22,23,24)(25,27,26)(28,29,30)(31,32,33)(34,35,36)$ |
| $C_3^7.S_3^2\wr C_2$ | 3L | $3$ | $72$ | not computed | 3L | 1A | $(4,6,5)(10,11,12)(13,14,15)(16,18,17)(19,20,21)(22,24,23)(25,27,26)(28,29,30)(31,32,33)(34,36,35)$ |
| $C_3^7.S_3^2\wr C_2$ | 3M | $3$ | $72$ | not computed | 3M | 1A | $(7,31,19)(8,32,21)(9,33,20)(25,27,26)$ |
| $C_3^7.S_3^2\wr C_2$ | 3N | $3$ | $72$ | not computed | 3N | 1A | $(7,32,19)(8,33,21)(9,31,20)(13,14,15)(25,26,27)$ |
| $C_3^7.S_3^2\wr C_2$ | 3O | $3$ | $72$ | not computed | 3O | 1A | $(1,3,2)(7,32,19)(8,33,21)(9,31,20)(13,15,14)(25,27,26)$ |
| $C_3^7.S_3^2\wr C_2$ | 3P | $3$ | $72$ | not computed | 3P | 1A | $(19,21,20)(22,23,24)(31,33,32)(34,36,35)$ |
| $C_3^7.S_3^2\wr C_2$ | 3Q1 | $3$ | $108$ | not computed | 3Q-1 | 1A | $(16,18,17)(19,20,21)(22,23,24)(28,30,29)(31,32,33)(34,36,35)$ |
| $C_3^7.S_3^2\wr C_2$ | 3Q-1 | $3$ | $108$ | not computed | 3Q1 | 1A | $(16,17,18)(19,21,20)(22,24,23)(28,29,30)(31,33,32)(34,35,36)$ |
| $C_3^7.S_3^2\wr C_2$ | 3R | $3$ | $144$ | not computed | 3R | 1A | $(7,9,8)(16,18,17)(19,20,21)(22,24,23)(28,30,29)(31,33,32)(34,35,36)$ |
| $C_3^7.S_3^2\wr C_2$ | 3S | $3$ | $144$ | not computed | 3S | 1A | $(1,15,27)(2,14,26)(3,13,25)(4,6,5)(7,9,8)(10,11,12)(16,18,17)(19,20,21)(22,24,23)(28,29,30)(34,36,35)$ |
| $C_3^7.S_3^2\wr C_2$ | 3T | $3$ | $144$ | not computed | 3T | 1A | $(1,13,27)(2,15,26)(3,14,25)(4,5,6)(7,9,8)(10,12,11)(16,17,18)(19,21,20)(22,23,24)(28,30,29)(31,32,33)(34,35,36)$ |
| $C_3^7.S_3^2\wr C_2$ | 3U | $3$ | $144$ | not computed | 3U | 1A | $(1,2,3)(4,30,18)(5,29,16)(6,28,17)(7,9,8)(10,11,12)(13,15,14)(19,20,21)(22,23,24)(25,27,26)(31,33,32)(34,35,36)$ |
| $C_3^7.S_3^2\wr C_2$ | 3V | $3$ | $144$ | not computed | 3V | 1A | $(1,2,3)(7,9,8)(10,36,23)(11,35,22)(12,34,24)(13,15,14)(16,17,18)(19,20,21)(25,27,26)(28,30,29)(31,33,32)$ |
| $C_3^7.S_3^2\wr C_2$ | 3W | $3$ | $144$ | not computed | 3W | 1A | $(1,2,3)(7,8,9)(10,36,24)(11,35,23)(12,34,22)(13,15,14)(19,21,20)(25,27,26)(28,29,30)(31,32,33)$ |
| $C_3^7.S_3^2\wr C_2$ | 3X | $3$ | $144$ | not computed | 3X | 1A | $(1,15,25)(2,14,27)(3,13,26)(4,5,6)(7,8,9)(10,11,12)(16,17,18)(22,24,23)(28,30,29)(34,36,35)$ |
| $C_3^7.S_3^2\wr C_2$ | 3Y1 | $3$ | $144$ | not computed | 3Y-1 | 1A | $(4,5,6)(10,11,12)(16,18,17)(19,20,21)(22,24,23)(31,32,33)(34,36,35)$ |
| $C_3^7.S_3^2\wr C_2$ | 3Y-1 | $3$ | $144$ | not computed | 3Y1 | 1A | $(4,6,5)(10,12,11)(16,17,18)(19,21,20)(22,23,24)(31,33,32)(34,35,36)$ |
| $C_3^7.S_3^2\wr C_2$ | 3Z | $3$ | $162$ | not computed | 3Z | 1A | $(13,15,14)(16,17,18)(19,20,21)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)$ |
| $C_3^7.S_3^2\wr C_2$ | 3AA1 | $3$ | $216$ | not computed | 3AA-1 | 1A | $(7,9,8)(13,15,14)(16,18,17)(19,20,21)(22,23,24)(25,26,27)(28,30,29)(31,33,32)(34,36,35)$ |
| $C_3^7.S_3^2\wr C_2$ | 3AA-1 | $3$ | $216$ | not computed | 3AA1 | 1A | $(7,8,9)(13,14,15)(16,17,18)(19,21,20)(22,24,23)(25,27,26)(28,29,30)(31,32,33)(34,35,36)$ |
| $C_3^7.S_3^2\wr C_2$ | 3AB | $3$ | $288$ | not computed | 3AB | 1A | $(7,8,9)(10,11,12)(13,14,15)(16,18,17)(19,21,20)(22,24,23)(25,27,26)(28,30,29)(31,32,33)(34,36,35)$ |
| $C_3^7.S_3^2\wr C_2$ | 3AC | $3$ | $288$ | not computed | 3AC | 1A | $(7,8,9)(10,22,35)(11,24,34)(12,23,36)(19,21,20)(28,30,29)(31,32,33)$ |
| $C_3^7.S_3^2\wr C_2$ | 3AD | $3$ | $288$ | not computed | 3AD | 1A | $(7,8,9)(10,22,34)(11,24,36)(12,23,35)(16,18,17)(19,21,20)(28,29,30)(31,32,33)$ |
| $C_3^7.S_3^2\wr C_2$ | 3AE | $3$ | $288$ | not computed | 3AE | 1A | $(4,5,6)(7,8,9)(10,22,35)(11,24,34)(12,23,36)(16,17,18)(19,21,20)(28,29,30)(31,32,33)$ |
| $C_3^7.S_3^2\wr C_2$ | 3AF | $3$ | $324$ | not computed | 3AF | 1A | $(1,2,3)(7,9,8)(10,12,11)(13,14,15)(16,18,17)(28,30,29)(31,32,33)(34,36,35)$ |
| $C_3^7.S_3^2\wr C_2$ | 3AG1 | $3$ | $432$ | not computed | 3AG-1 | 1A | $(7,33,19)(8,31,21)(9,32,20)(10,12,11)(22,24,23)(25,27,26)$ |
| $C_3^7.S_3^2\wr C_2$ | 3AG-1 | $3$ | $432$ | not computed | 3AG1 | 1A | $(7,19,33)(8,21,31)(9,20,32)(10,11,12)(22,23,24)(25,26,27)$ |
| $C_3^7.S_3^2\wr C_2$ | 3AH1 | $3$ | $432$ | not computed | 3AH-1 | 1A | $(1,3,2)(4,17,29)(5,18,28)(6,16,30)(10,12,11)(22,23,24)(25,27,26)$ |
| $C_3^7.S_3^2\wr C_2$ | 3AH-1 | $3$ | $432$ | not computed | 3AH1 | 1A | $(1,2,3)(4,29,17)(5,28,18)(6,30,16)(10,11,12)(22,24,23)(25,26,27)$ |